A body of density d is counterpoised by Mg of weights of density `d_1` in air of density d. Then the true mass of the body is

Options

A. M
B. `M(1-(d)/(d_2))`
C. `M(1-(d)/(d_1))`
D. `(M(1-d//d_2))/((1-d//d_1))`

Answer

D

Explanation

`M_0 rarr` Mass of body in vacuum
Apparent weight of the body in air = Apparent weight of standard weight in air
`implies` Actual weight-upthrust due to displaced air
`implies M_0 g-((M_0)/(d_1))dg=Mg-((M)/(D_2))dg implies M_0=(M[1-(d)/(d_2)])/([1-(d)/(d_1)])`